Abstract
This paper considers a left-continuous dynamical system and exponential stability of periodic orbits in the system. Firstly, we introduce new continuity concepts with respect to initial conditions, and prove their equivalence conditions. Under the equivalence conditions, it is useful for analysis of exponential stability of hybrid periodic orbits to use those continuities differently according to where discontinuous jumps exist. Finally, we prove equivalence between exponential stability for a periodic orbit, and that for a fixed point of the generalized Poincaré map by applying the analysis method based on the proposed continuities.
